Let (R; m;k) be a local ring (commutative and Noetherian). We will discuss existence and uniqueness of direct-sum decompositions of nitely generated R-modules. One says that R has nite CM type provided there are only nitely many indecomposable maximal Cohen-Macaulay R-modules up to isomorphism. Among complete equicharacteristic hypersurface rings with k algebraically closed of characteristic 6 ...

Let S be an unramified regular local ring of mixed characteristic two and R the integral closure in a biquadratic extension its quotient field obtained by adjoining roots sufficiently general square free elements f,g?S. S2 denote subring lifting to image Frobenius map on S/2S. When at least one f,g?S2, we characterize Cohen-Macaulayness show that admits birational small Cohen-Macaulay module. I...

We investigate lifting i e the process of taking a valid inequality for a polyhe dron and extending it to a valid inequality in a higher dimensional space Lifting is usually applied sequentially that is variables in a set are lifted one after the other This may be computationally unattractive since it involves the solution of an optimization problem to compute a lifting coe cient for each varia...

We obtain a presentation of the principal subspace of the basic A (2) 2n –module, n ≥ 1. We show that its full character is given by the Nahm sum of the tadpole Dynkin diagram Tn = A2n/Z2. This character is conjecturally modular after certain specializations. We prove the modularity property in the case of the affine Lie algebra of type A (2) 4 .

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms, indecomposable finitely-generated Gorenstein-projective A-modules. We prove that for a Gorenstein artin algebra, it is CM-finite if and only if every its Gorenstein-projective module is a direct sum of finitely-generated Gorenstein-projective modules.

Let Γ denote a Q-polynomial distance-regular graph with diameter at least three and standard module V . We introduce two direct sum decompositions of V . We call these the displacement decomposition for Γ and the split decomposition for Γ. We describe how these decompositions are related.

Radio Detection and Ranging (Radar) is an electromagnetic wave used to monitor the movement of a moving object. RADAR will get information about height distance object by utilizing waves. Radar surveillance equipment aircraft’s position in environment around radar up radius ± 250 NM. This article aims analyze facility at Kualanamu Airport Monopulse Secondary Surveillance (MSSR) INDRA. paper use...

The G-module structure of the cohomology groups of line bundles over the flag variety G/B for a semisimple algebraic group G is studied. It is proved that, generically, their socle filtrations satisfy the same sum formula as Andersen’s filtrations if Lusztig’s conjecture is true. Another purpose of this paper is to calculate the socle series of the H0’s for the p-regular weights close to a cham...